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Simplifying x2 + 144x + -144 = 0 Reorder the terms: -144 + 144x + x2 = 0 Solving -144 + 144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 144x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 144x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 144x + x2 = 0 + 144 144x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 144x + x2 = 144 The x term is 144x. Take half its coefficient (72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. 144x + 5184 + x2 = 144 + 5184 Reorder the terms: 5184 + 144x + x2 = 144 + 5184 Combine like terms: 144 + 5184 = 5328 5184 + 144x + x2 = 5328 Factor a perfect square on the left side: (x + 72)(x + 72) = 5328 Calculate the square root of the right side: 72.993150364 Break this problem into two subproblems by setting (x + 72) equal to 72.993150364 and -72.993150364.Subproblem 1
x + 72 = 72.993150364 Simplifying x + 72 = 72.993150364 Reorder the terms: 72 + x = 72.993150364 Solving 72 + x = 72.993150364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = 72.993150364 + -72 Combine like terms: 72 + -72 = 0 0 + x = 72.993150364 + -72 x = 72.993150364 + -72 Combine like terms: 72.993150364 + -72 = 0.993150364 x = 0.993150364 Simplifying x = 0.993150364Subproblem 2
x + 72 = -72.993150364 Simplifying x + 72 = -72.993150364 Reorder the terms: 72 + x = -72.993150364 Solving 72 + x = -72.993150364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = -72.993150364 + -72 Combine like terms: 72 + -72 = 0 0 + x = -72.993150364 + -72 x = -72.993150364 + -72 Combine like terms: -72.993150364 + -72 = -144.993150364 x = -144.993150364 Simplifying x = -144.993150364Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.993150364, -144.993150364}
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